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Theoria motus corporum solidorum seu rigidorum ex primis nostrae cognitionis principiis stabilita et ad omnes motus, qui in huiusmodi corpora cadere possunt, accommodata / auctore Leonh. Eulero
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basi sphaerica praeditor. SUPER &c. 4-z

Ex his fi ponatur arcus ZD >=:.(>, erit

Scof! 2 co[Qt + g) 2 , fini 2 coQ>t + H) 2 "X? ~ \ cofg 2 coff} 2 J

Cof/— Cof?CoD> P-\‘?PP «>f?

Porro ex triangulo AZD cfl cof ADZ—— =--—-—

lin^fin^ ^ nn?

n s cof?

evnnefceute termino — — —, hinc ergo erit

? fin £

cof ADZ =

+

2 liti ^

cofl C of(<?f + 3) . y- ^ cof(i Cof (^ + 8)*

L:/(

_ „ 0

cof fp z J

cofg tangi cof(^t -f- h)

coig

fini 2 cof(^+ h)

cofg 2

ideoquc tang ADZ =

corf) coi(<)/-f Q)

Praeter .arcum autem DZ = ^ et angulum ADZ nofle oportet angulumXZD a circulo verticali fixo ZX computatum ; efi vero DZA = i#o°

_ _ — cofrt cof(<]V 4 - h) . . . ,t

— ADZ, leu tang DZA —-„- tangi, cum initio ellet

’ ° eof h coi (it 4-g) S

DZA =r Igo 0 _ l et tangDZA = — tangi. Deinde vero pofito angulo— df iit cofw 4- z co(5- ydt

XZA = A, eftrfA= --h>»cqucA =

Conft,.

s t (aa cofn cof?- ce cofb fin?) r cofg 1 fini cof(^+ h)

~aa cof? 2 + tc fin ? 2 ceu 1 fin cofh

Qiiodfi ponamus initio angulum XZD evanuifie, initio fuerat A = J$o°l, fi eque conflans hic iugrefla efi:

rcof? fini

Confi. =s 18o° - I 4 - 55

unde habebimus:A= 180° -l-

(l-

ceu 1 fin ?

et (an cofn cof? — rr cofb fin?)

aa cof? 2 4-« fin? 2cof(<h 4 - h) ^

r cof? fin fccu' fin ?

coi h

hineque XZD = A — DZA, ex quibus ad tempus t fitus corporis perfeflecognofeitur, in hacque determinatione finnii motus continetur,

COROLL.